{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. 简述仿射变换和透视变换的基本概念，并用实例说明。 "
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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jTwJoAzQNqKC0ZRcnX/SM3rcHAYQBfwhehEJqYwZkAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgAiZgArtN4P+uExwVMBQ0UgAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "仿射变换是一种二维坐标到二维坐标之间的线性变换，它保持了二维图形的“平直性”（直线经过变换之后依然是直线）和“平行性”（二维图形之间的相对位置关系保持不变，平行线依然是平行线，且直线上点的位置顺序不变）。任意的仿射变换都能表示为乘以一个矩阵(线性变换)，再加上一个向量 (平移) 的形式。\n",
    "\n",
    "透视变换是将图片投影到一个新的视平面，也称作投影映射。它是二维（x,y）到三维(X,Y,Z)，再到另一个二维(x’,y’)空间的映射。\n",
    "\n",
    "仿射变换后平行四边形的各边仍操持平行，透视变换结果允许是梯形等四边形，所以仿射变换是透视变换的子集。\n",
    "\n",
    "仿射变换：![image.png](attachment:image.png)\n",
    "透视变换：![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. 结合图简述图像坐标系、相机坐标系和世界坐标系的定义，并说明三者之间的变换关系。 "
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "世界坐标系：客观三维世界的绝对坐标系，也称客观坐标系。因为数码相机安放在三维空间中，我们需要世界坐标系这个基准坐标系来描述数码相机的位置，并且用它来描述安放在此三维环境中的其它任何物体的位置，用（X, Y, Z）表示其坐标值。\n",
    "\n",
    "相机坐标系：以相机的光心为坐标原点，X 轴和Y 轴分别平行于图像坐标系的 X 轴和Y 轴，相机的光轴为Z 轴，用（Xc, Yc, Zc）表示其坐标值。\n",
    "\n",
    "图像坐标系：以CCD 图像平面的中心为坐标原点，X轴和Y 轴分别平行于图像平面的两条垂直边，用( x , y )表示其坐标值。图像坐标系是用物理单位（例如毫米）表示像素在图像中的位置。\n",
    "\n",
    "世界坐标系转为相机坐标系：\n",
    "世界坐标系到相机坐标系，涉及到旋转和平移（其实所有的运动也可以用旋转矩阵和平移向量来描述）。绕着不同的坐标轴旋转不同的角度，得到相应的旋转矩阵，如下图所示： \n",
    "![image.png](attachment:image.png)\n",
    "那么从世界坐标系到相机坐标系的转换关系如下所示：\n",
    "![image.png](attachment:image.png)\n",
    "相机坐标系转为图像坐标系：\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. 什么是相机的内、外参数矩阵？实际中你能结合身边的实例(如电脑摄像头、手机镜头)说明这些参数的大致值么？ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "相机内参数是与相机自身特性相关的参数，比如相机的焦距、像素大小等；\n",
    "\n",
    "相机外参数是在世界坐标系中的参数，比如相机的位置、旋转方向等。\n",
    "参数：\n",
    "\n",
    "采用焦距f​：50 mm\n",
    "分辨率采用：1920x1080\n",
    "传感器尺寸：22.5x15 mm\n",
    "计算内参数：\n",
    "u0=19202=960​、v0=10802=540​、dx=22.51920=0.0117​、dy=151080=0.0139​\n",
    "ax=fdx=4266.67、ay=fdy=360"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. 说明使用线性法求解相对位姿时的要求输入和输出，以及求解的基本思想。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "输入：相机的内参数；多个空间上的特征点(非共面)在目标坐标系(3D)和相平面坐标系(2D)坐标。\n",
    "输出：目标坐标系相对相机坐标系的位置和姿态。\n",
    "\n",
    "通过相机标定或者相机自身参数计算获取相机内参数和畸变系数，建立世界坐标系转换为像素坐标系的方程。目的是求解外参数矩阵的旋转向量和平移向量\n",
    "通过方程组的变换，消去第三维的坐标，最后得到一个关于旋转向量和平移向量的公式。扩展到多个点的情况下，有六个或以上的特征点且非共面的时候，就可解得一个关于旋转向量和平移向量的矩阵组。利用矩阵的QR分解，得到最终的旋转矩阵和平移矩阵。最后通过旋转矩阵计算旋转角，使得相机坐标系和世界坐标系完全平行。\n",
    "注意：在实现过程中，一般使用solvePnP方法进行计算，传入参数：目标坐标系的3D点，图像平面点坐标，相机内参数，畸变系数，最后就可以得到旋转向量和平移向量。"
   ]
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   "source": [
    "### 5.5. 说明使用Zhang方法进行相机标定需要的输入条件和得到的具体输出量，以及Zhang方法的主要步骤. "
   ]
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    "输入条件：目标物体的多个pose的图片数据，一般最少30张。通过图片数据，获取目标坐标系的3D点和图像平面点坐标。\n",
    "\n",
    "输出量：相机内参数矩阵；畸变系数；旋转变量；平移变量。\n",
    "\n",
    "主要步骤：设定标定板；旋转标定板或相机，采集标定板图像的不同pose；对一个pose,计算单应矩阵(类似M矩阵)；有三个以上Pose，根据各单应矩阵计算线性相机参数；使用非线性优化方法计算非线性参数；最后得到相机内参数、矩阵畸变系数以及每张图片的旋转变量和平移变量。"
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